The Web courier went belly up in 2001, less than four years after it introduced its service promising to deliver to customers’ doorsteps just about anything they wanted in about an hour. Kozmo raised more than $250 million in financing from venture-capital firms, and from heavyweights including Starbucks Corp. and Amazon.com Inc., en route to a planned initial public offering before falling under the weight of an overly ambitious expansion.

Kozmo had been an overnight sensation. By eschewing delivery charges or minimum order sizes, Kozmo drew a wide swath of customers, including some wanting, say, a lone DVD or candy bar to satisfy the late-night munchies. The company sold brand-name products from its own distribution centers.

But Kozmo expanded into too many markets too quickly, said Kozmo co-founder Joseph Park, now the chief executive of Bluefly Inc., a designer clothing website.

“The one disadvantage that e-commerce has versus shopping in a physical store is instant gratification, at least for physical products,” says Mr. Park. “Today, it’s still a compelling idea that you could get all the benefits of online shopping and combine that with the one of the most important aspects of offline shopping: getting your merchandise immediately.”

Kozmo also was slow to implement delivery fees and minimum order sizes, Mr. Park said. When it eventually did, Kozmo charged $2 per delivery with a minimum of a $5 order. But it was too late.

Kozmo’s costs far exceeded its revenue. When the company filed for an initial public offering in March 2000, it revealed revenue for the prior year was $3.5 million with losses totaling $29 million.

“The question remains: ‘How do you do this profitably?’” Mr. Park said.

That’s a question eBay Inc Wal-Mart Stores Inc., Amazon.com Inc. and a host of startups will have to answer as they roll out same-day delivery services in cities like San Francisco, New York, Chicago and Seattle.

Under eBay’s model, known as eBay Now, couriers pick up merchandise at area stores like Target and Macy’s and deliver them to customers within an hour. That means, unlike Kozmo, it won’t have to maintain costly warehouses, but will instead have to profit from the $5 delivery charges. The minimum order is $25, and eBay pays the couriers about $12.50 per hour, plus 55 cents per mile driven. For eBay Now to be profitable, its couriers will likely have to deliver several items per hour.

Today, eBay Now is operating only in New York and San Francisco, but the company has said it may introduce the service in other cities and could extend it to the concert t-shirts, action figures and other ephemera that made eBay famous.

Wal-Mart, of course, has thousands of stores across the U.S. serving as possible warehouses and has the expedited same-day delivery service — for $5 to $10 per order — in only a handful of cities. Amazon, which has offered same-day delivery since 2009 in a few select cities, has said it hasn’t figured out how to feasibly roll out same-day shipping on a broad scale.

David Puck, 35-years-old, who worked as a courier for Kozmo in Chicago from 2000 to 2001, says he thought the company might have survived if it hadn’t expanded so rapidly. “The company’s vision was dead-on,” he said. “They just got too big.

“They got caught up in the whole dotcom bubble and probably were just in the wrong place at the wrong time” he said. “Customers really loved it.”

Kozmo also paid its messengers handsomely, Mr. Puck says, noting the $9-per-hour paycheck, plus $1 for each delivery, as well as health insurance, 401(k)s and pricey Columbia brand jackets, gloves and pants to help withstand the Chicago winters. In its later stages, Kozmo furnished its messengers with scooters and began selling cigarettes.

“The worst days were Sunday mornings when you’d have people ordering a gallon of milk, orange juice and donuts,” says Mr. Puck. “When you have four of those orders on your back, it gets pretty damn heavy.”

Still, he says he recalled delivering single packs of gum to some customers who were curious about the service. Mr. Puck made a delivery nearly every day to one customer who ordered a DVD and various snacks. “He would offer to tip me with a [marijuana] joint,” says Mr. Puck.